PPML, Gravity, and Heterogeneous Trade Elasticities

We revisit the gravity equation, the most widely used empirical tool in international trade, and show that common estimators recover distinct parameters when trade elasticities are heterogeneous: Poisson pseudo-maximum likelihood (PPML) estimates the aggregate elasticity, while ordinary least squares (OLS) and Gamma PML estimate the average elasticity. We demonstrate that, contrary to common belief, differences between OLS and PPML estimates are driven primarily by elasticity heterogeneity rather than heteroskedasticity of an error term or inclusion of zero trade flows. We develop a simple test for heterogeneity and, applying it to disaggregated trade data, reject homogeneity in at least 57% of industries. We then introduce a weighted PPML (WPPML) estimator to recover the aggregate effects of arbitrary, non-uniform shocks. Using WPPML, we show that trade flows respond less to realized tariff reductions from 2001-2016 than to uniform liberalization, reflecting systematic selection in where barriers fall, with substantial variation across industries.